Efficient Algorithms for the (Weighted) Minimum Circle Problem

The (weighted) minimum covering circle problem is a well-known single facility location problem used in emergency facility models. This paper introduces a classification scheme, based on fundamental mathematical programming concepts, for algorithms which solve both weighted and unweighted versions. One result of this classification is proof that a recently developed method is identical to one developed in the nineteenth century. Also, within the classification scheme, efficient new algorithms are given for the weighted problem. The results of some extensive computational tests identify the (empirically) fastest methods.